Edge infrastructure and Industry 4.0 required services are offered by edge-servers (ESs) with different computation capabilities to run social application's workload based on a leased-price method. The usage of Social Internet of Things (SIoT) applications increases day-to-day, which makes social platforms very popular and simultaneously requires an effective computation system to achieve high service reliability. In this regard, offloading high required computational social service requests (SRs) in a time slot based on directed acyclic graph (DAG) is an NP-complete problem. Most state-of-art methods concentrate on the energy preservation of networks but neglect the resource sharing cost and dynamic subservice execution time (SET) during the computation and resource sharing. This article proposes a two-step deep reinforcement learning (DRL)-based service offloading (DSO) approach to diminish edge server costs through a DRL influenced resource and SET analysis (RSA) model. In the first level, the service and edge server cost is considered during service offloading. In the second level, the R-retaliation method evaluates resource factors to optimize resource sharing and SET fluctuations. The simulation results show that the proposed DSO approach achieves low execution costs by streamlining dynamic service completion and transmission time, server cost, and deadline violation rate attributes. Compared to the state-of-art approaches, our proposed method has achieved high resource usage with low energy consumption.